Abstract

A strictly barrelled disk B in a Hausdorff locally convex space E is
a disk such that the linear span of B with the topology of the Minkowski
functional of B is a strictly barrelled space. Valdivia's closed graph theorems
are used to show that closed strictly barrelled
disk in a quasi-(LB)-space is
bounded. It is shown that a locally strictly
barrelled quasi-(LB)-space is
locally complete. Also, we show that a regular
inductive limit of quasi-(LB)-spaces is locally complete if and only if each closed bounded disk is a strictly
barrelled disk in one of the constituents.

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